The Stability of the Minisuperspace

TL;DR

This paper investigates the stability of the early universe's minisuperspace model by numerically solving the Wheeler-DeWitt equation, revealing stability at large scales and instability near the Planck length.

Contribution

It demonstrates the stability conditions of the minisuperspace model by incorporating inhomogeneous modes and numerical analysis of the Wheeler-DeWitt equation.

Findings

Minisuperspace is stable when the scale factor exceeds a few times the Planck length.

Instability occurs when the scale factor is comparable to the Planck length.

Numerical solutions effectively incorporate inhomogeneous wave modes.

Abstract

The stability of the minisuperspace model of the early universe is studied by solving the Wheeler-DeWitt equation numerically. We consider a system of Einstein gravity with a scalar field. When we solve the Wheeler-DeWitt equation, we pick up some inhomogeneous wave modes from the infinite number of modes adequately: degrees of freedom of the superspace are restricted to a finite one. We show that the minisuperspace is stable when a scale factor ($a$) of the universe is larger than a few times of the Planck length, while it becomes unstable when $a$ is comparable to the Planck length.